If you kill a monster, your MF affects your drops. If your merc kills a monster, their effective MF is a sum of your MF and their MF. So giving them MF equipment will increase their chances of good stuff, but only on things they kill themselves.

I don't have a complete list of things they aren't affected by. However, I know they have no mana at all, so anything with +mana, or +energy (or anything related) wouldn't affect them. In addition, they don't have vitality, so anything with +vitality won't affect them, either.